# Forward versus Backward: Comparing Reasoning Objectives in Direct Preference Optimization

arXiv: https://arxiv.org/abs/2601.07199 · HTML: https://mlsanity.com/paper/2601.07199/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 13 of its 15 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 13 of 13)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Reverse Chain: A Generic-Rule for LLMs to Master Multi-API Planning](https://mlsanity.com/paper/2310.04474/) (2023)

## Abstract (arXiv)

Large language models exhibit impressive reasoning capabilities yet frequently generate plausible but incorrect solutions, a phenomenon commonly termed hallucination. This paper investigates the effect of training objective composition on reasoning reliability through Direct Preference Optimization. Two complementary training signals are examined: forward chain-of-thought generation, which trains the model to produce correct reasoning traces, and backward verification, which trains the model to verify and acknowledge errors in candidate solutions. Experiments on GSM8K reveal a fundamental trade-off between these objectives. Forward-only DPO training achieves the highest accuracy improvement, increasing from 83.1% to 86.6% (+3.5 percentage points), while backward-only training yields minimal accuracy gains but substantially reduces the false positive rate from 13.4% to 4.3%. Notably, both training variants reduce acknowledgement rate compared to the baseline, suggesting that preference optimization increases model confidence in its outputs. These findings indicate that forward and backward reasoning objectives provide distinct and complementary learning signals: forward training improves problem-solving capability, while backward training improves verification calibration. The complete training and evaluation pipeline, implemented efficiently through Low-Rank Adaptation, is released to facilitate further research.